We present a novel recurrent neural network (RNN) architecture that combines the remembering ability of unitary RNNs with the ability of gated RNNs to effectively forget redundant information in the input sequence. We achieve this by extending Unitary RNNs with a gating mechanism. Our model is able to outperform LSTMs, GRUs and Unitary RNNs on different benchmark tasks, as the ability to simultaneously remember long term dependencies and forget irrelevant information in the input sequence helps with many natural long term sequential tasks such as language modeling and question answering. We provide competitive results along with an analysis of our model on the bAbI Question Answering task, PennTreeBank, as well as synthetic tasks that involve long-term dependencies such as parenthesis, denoising and copying tasks.